In this study, an analysis has performed for heat and mass transfer of a steady laminar boundary-layer flow of an electrically magnetic conducting fluid of second-grade subject to suction and to a transverse uniform magnetic and electric field past a semi-infinite stretching sheet. Parameters Gr; Gc; E1; M; Sc which are used to represent the dominance of the buoyant effect, magnetic effect, electric effect and mass transfer effect are present in governing equations, respectively. The novelty of the present work is considered the mass transfer phenomena to a coupled heat and mass transfer boundary-layer equations. The similar transformation and the finite-difference method are used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature profiles, the wall unknown values of h 0 Γ°0Γ and / 0 Γ°0Γ for calculating the heat and mass transfer of the similar boundary-layer flow are carried out as functions of the visco-elastic parameter E, the Prandtl number Pr, the buoyancy parameters Gr; Gc and mass transfer coefficient Sc. The value of E; Pr; E1; Gr; Gc and Sc parameter are important factors in this study. It will produce greater heat transfer efficiency with a larger value of those parameters, but the magnetic parameter M may reduce the heat transfer efficiency. On the other hand, for mass transfer, the value of Sc parameter is important factor in this study. It will produce greater heat transfer efficiency with a larger value of Sc.